How to render static and animated objects separately to save render time?
So.. You should use 'View Layers' (https://docs.blender.org/manual/en/latest/render/layers/layers.html).
As said above in the comments by @Bruno you should render the still as an image, on the other view layer render the animation with shadow catcher and in the video editor (VSE) add them together to a video.

(to be honest you can probably just render them separately and attach them together later in the VSE just as long as you keep original scene.)

I am attaching link to a demo scene, hope it helps. (https://drive.google.com/file/d/10fXBH4o2sz4b0ceBPyRouquxhjgi_8gZ/view?usp=sharing)